When taking hydrometer readings, does the part of the carboy the sample comes from have a large impact on the actual reading?

For example, I took a reading about 4 hours after my boil, from the very top of the carboy. Is there a chance what I see here is significantly less dense than the liquid towards the bottom at this early stage, before fermentation has begun?

The wort should be thoroughly mixed and oxygenated prior to taking your hydrometer reading. It's certainly possible for the readings to be different from different parts of the fermenter if you don't properly mix the solution....haven't you ever read the OG questions in Beginner's Forum?